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notes.tex

Timestamp:

Jan 3, 2009, 7:09:11 PM (16 years ago)

Author:

Xavier Rouby

Message:

two column; chap1,2 ok. chap3 ok sauf Etmis. validation presque ok

File:

: 1 edited

trunk/paper/notes.tex (modified) (25 diffs)

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trunk/paper/notes.tex

-              r120
+              r121
 \documentclass[a4paper,11pt,oneside,onecolumn]{article}
+\documentclass[a4paper,11pt,oneside,twocolumn]{article}
 %\usepackage[english]{babel}
 \usepackage[ansinew]{inputenc}
 %\usepackage{abstract}
+\usepackage{abstract}
 \usepackage{amsmath}
 …
 \usepackage{fancyhdr}
 \usepackage{verbatim}
 \addtolength{\textwidth}{2cm} \addtolength{\hoffset}{-1cm}
+\addtolength{\textwidth}{1cm} \addtolength{\hoffset}{-0.5cm}
 \usepackage[colorlinks=true, pdfstartview=FitV, linkcolor=black, citecolor=black, urlcolor=black, unicode]{hyperref}
 \usepackage{ifpdf}
 …
 \begin{document}
+\twocolumn[
 \maketitle
+\begin{abstract}
 Knowing whether theoretical predictions are visible and measurable in a high energy experiment is always delicate, due to the
 complexity of the related detectors, data acquisition chain and software. We introduce here a new framework, \textsc{Delphes}, for fast simulation of
 …
 \textit{Keywords:} \textsc{Delphes}, fast simulation, LHC, smearing, trigger, \textsc{FastJet}, \textsc{Hector}, \textsc{Frog}
 \vspace{1cm}
+%\saythanks
+\end{abstract}
+]
+\saythanks
 \section{Introduction}
 …
 A new framework, called \textsc{Delphes}~\cite{bib:Delphes}, is introduced here, for the fast simulation of a general purpose collider experiment.
 Using the framework, observables can be estimated for specific signal and background channels, as well as their production and measurement rates, under a set of assumptions.
 Starting from the output of event generators, the simulation of the detector response takes into account the subdetector resolutions, by smearing the kinematical properties of the visible final particles. Tracks of charged particles and calorimetric towers are then created.
+Starting from the output of event generators, the simulation of the detector response takes into account the subdetector resolutions, by smearing the kinematical properties of the visible final particles. Tracks of charged particles and calorimetric towers (or \textit{calotowers} are then created.
 \textsc{Delphes} includes the most crucial experimental features, like (1) the geometry of both central or forward detectors; (2) lepton isolation; (3) reconstruction of photons, leptons, jets, $b$-jets, $\tau$-jets and missing transverse energy; (4) trigger emulation and (5) an event display (Fig.~\ref{fig:FlowChart}).
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=0.9\columnwidth]{FlowDelphes}
+\begin{figure*}[t]
+\begin{center}
+%\includegraphics[width=0.9\textwidth]{FlowDelphes}
+\includegraphics[scale=0.78]{FlowDelphes}
 \caption{Flow chart describing the principles behind \textsc{Delphes}. Event files coming from external Monte Carlo generators are read by a convertor stage.
 The kinematical variables of the final state particles are then smeared according to the subdetector resolutions.
 …
 \label{fig:FlowChart}
 \end{center}
 \end{figure}
+\end{figure*}
 Although this kind of approach yields much realistic results than a simple ``parton-level" analysis, a fast simulation comes with some limitations. Detector geometry is idealised, being uniform, symmetric around the beam axis, and having no cracks nor dead material. Secondary interactions, multiple scatterings, photon conversion and bremsstrahlung are also neglected.
 …
 \section{Detector simulation}
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=\columnwidth]{Detector_Delphes_1}
+\caption{Layout of the generic detector geometry assumed in \textsc{Delphes}. The innermost layer, close to the interaction point, is a central tracking system (pink).
+It is surrounded by a central calorimeter volume (green) with both electromagnetic and hadronic sections.
+The outer layer of the central system (red) consist of a muon system. In addition, two end-cap calorimeters (blue) extend the pseudorapidity coverage of the central detector.
+The actual detector granularity and extension is defined in the user-configuration card. The detector is assumed to be strictly symmetric around the beam axis (black line). Additional forward detectors are not depicted.}
+\label{fig:GenDet}
+\end{center}
+\end{figure}
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=0.5\columnwidth]{Detector_Delphes_3}
+\caption{Profile of the layout assumed in \textsc{Delphes}. The extension of the various subdetectors, as defined in Tab.~\ref{tab:defEta}, are clearly visible.
+Same colour codes as for Fig.~\ref{fig:GenDet} are applied. Additional forward detectors are not depicted.}
+\label{fig:GenDet3}
+\end{center}
+\end{figure}
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=0.6\columnwidth]{Detector_Delphes_2b}
+\caption{Layout of the generic detector geometry assumed in \textsc{Delphes}. Open 3D-view of the detector with solid volumes. Same colour codes as for Fig.~\ref{fig:GenDet} are applied. Additional forward detectors are not depicted.}
+\label{fig:GenDet2}
+\end{center}
+\end{figure}
+The overall layout of the general purpose detector simulated by \textsc{Delphes} is shown in figure \ref{fig:GenDet}.
+The overall layout of the general purpose detector simulated by \textsc{Delphes} is shown in Fig.~\ref{fig:GenDet3}.
 A central tracking system (\textsc{tracker}) is surrounded by an electromagnetic and a hadron calorimeters (\textsc{ecal} and \textsc{hcal}, resp.). Two forward calorimeters (\textsc{fcal}) ensure a larger geometric coverage for the measurement of the missing transverse energy. Finally, a muon system (\textsc{muon}) encloses the central detector volume
 The fast simulation of the detector response takes into account geometrical acceptance of sub-detectors and their finite resolution, as defined in the smearing data card\footnote{\texttt{[code] }See the \texttt{RESOLution} class.}.
 If no such file is provided, predifined values are used. The coverage of the various subsystems used in the default configuration are summarised in table \ref{tab:defEta}.
+\begin{table}[!h]
+\begin{table*}[t]
 \begin{center}
 \caption{Default extension in pseudorapidity $\eta$ of the different subdetectors.
 The corresponding parameter name, in the smearing card, is given. \vspace{0.5cm}}
 \begin{tabular}[!h]{lll}
+\begin{tabular}{lll}
 \hline
 \textsc{tracker} & {\verb CEN_max_tracker } & $0.0 \leq |\eta| \leq 2.5$\\
 …
 \label{tab:defEta}
 \end{center}
+\end{table}
+\end{table*}
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=\columnwidth]{Detector_Delphes_3}
+\caption{
+Profile of layout of the generic detector geometry assumed in \textsc{Delphes}. The innermost layer, close to the interaction point, is a central tracking system (pink).
+It is surrounded by a central calorimeter volume (green) with both electromagnetic and hadronic sections.
+The outer layer of the central system (red) consist of a muon system. In addition, two end-cap calorimeters (blue) extend the pseudorapidity coverage of the central detector.
+The detector parameters are defined in the user-configuration card. The extension of the various subdetectors, as defined in Tab.~\ref{tab:defEta}, are clearly visible. The detector is assumed to be strictly symmetric around the beam axis (black line). Additional forward detectors are not depicted.
+}
+\label{fig:GenDet3}
+\end{center}
+\end{figure}
+\subsubsection*{Magnetic field}
+In addition to the subdetectors, the effects of a dipolar magnetic field is simulated for the charged particles\footnote{\texttt{[code] }See the \texttt{TrackPropagation} class.}. This simply modifies the corresponding particle direction before it enters the calorimeters.
 \subsection{Tracks reconstruction}
 …
 The particle 4-momentum $p^\mu$ are smeared with a parametrisation directly derived from the detector techinal designs\footnote{\texttt{[code] }The response of the detector is applied to the electromagnetic and the hadronic particles through the \texttt{SmearElectron} and \texttt{SmearHadron} functions.}.
+The particle four-momentum $p^\mu$ are smeared with a parametrisation directly derived from the detector techinal designs\footnote{\texttt{[code] }The response of the detector is applied to the electromagnetic and the hadronic particles through the \texttt{SmearElectron} and \texttt{SmearHadron} functions.}.
 In the default parametrisation, the calorimeter is assumed to cover the pseudorapidity range $|\eta|<3$ and consists in an electromagnetic and an hadronic part. Coverage between pseudorapidities of $3.0$ and $5.0$ is provided by forward calorimeters, with different response to electromagnetic objects ($e^\pm, \gamma$) or hadrons.
 Muons and neutrinos are assumed no to interact with the calorimeters\footnote{In the current \textsc{Delphes} version, particles other than electrons ($e^\pm$), photons ($\gamma$), muons ($\mu^\pm$) and neutrinos ($\nu_e$, $\nu_\mu$ and $\nu_\tau$) are simulated as hadrons for their interactions with the calorimeters. The simulation of stable particles beyond the Standard Model should subsequently be handled with care.}.
 …
 The smallest unit for geometrical sampling of the calorimeters is a \textit{tower}; it segments the $(\eta,\phi)$ plane for the energy measurement.
 All undecayed particles, except muons and neutrinos produce a calorimetric tower, either in \textsc{ecal}, in \textsc{hcal} or \textsc{fcal}.
+As the detector is assumed to be symmetric in $\phi$ and with respect to the $\eta=0$ plane, the smearing card stores the number of calorimetric towers with $\phi=0$ and $\eta>0$ (default: $40$ towers). For a given $\eta$, the size of the $\phi$ segmentation is also specified.
+The calorimetric towers directly enter in the calculation of the missing transverse energy, and as input for the jet reconstruction algorithms.
+No longitudinal segmentation is available in the simulated calorimeters.
+No sharing between neighbouring towers is implemented when particles enter a tower very close to its geometrical edge.
+\textcolor{red}{Mettre une figure avec une grille en $(\eta,\phi)$ pour illustrer la segmentation (un peu comme une feuille quadrillÃ©e).}
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=0.8\columnwidth]{calosegmentation}
+As the detector is assumed to be symmetric in $\phi$ and with respect to the $\eta=0$ plane, the smearing card stores the number of calorimetric towers with $\phi=0$ and $\eta>0$ (default: $40$ towers). For a given $\eta$, the size of the $\phi$ segmentation is also specified. Fig.~\ref{fig:calosegmentation} illustrates the default segmentation of the $(\eta,\phi)$ plane.
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=\columnwidth]{calosegmentation}
 \caption{Default segmentation of the calorimeters in the $(\eta,\phi)$ plane. Only the central detectors (\textsc{ecal}, \textsc{hcal} and \textsc{fcal}) are considered.}
 \label{fig:calosegmentation}
 …
 \end{figure}
+The calorimetric towers directly enter in the calculation of the missing transverse energy, and as input for the jet reconstruction algorithms. No longitudinal segmentation is available in the simulated calorimeters. No sharing between neighbouring towers is implemented when particles enter a tower very close to its geometrical edge.
 \subsection{Very forward detectors simulation}
 …
 \begin{figure}[!h]
 \begin{center}
 \includegraphics[width=0.8\columnwidth]{fdets}
+\includegraphics[width=\columnwidth]{fdets}
 \caption{Default location of the very forward detectors, including \textsc{zdc}, \textsc{rp220} and \textsc{fp420} in the \textsc{lhc} beamline.
 Incoming (red) and outgoing (black) beams on one side of the interaction point ($s=0~\textrm{m}$).
 …
 \end{figure}
 \begin{table}[!h]
+\begin{table*}[t]
 \begin{center}
 \caption{Default parameters for the forward detectors: distance from the interaction point and detector acceptance. The \textsc{lhc} beamline is assumed around the fifth interaction point. For the \textsc{zdc}, the acceptance depends only on the pseudorapidity $\eta$ of the particle, which should be neutral and stable.
 The tagger acceptance is fully determined by the distance in the transverse plane of the detector to the real beam position~\cite{bib:Hector}. It is expressed in terms of the particle energy.
 \vspace{0.5cm}}
 \begin{tabular}[!h]{llcl}
+\begin{tabular}{llcl}
 \hline
 Detector & Distance & Acceptance & \\ \hline
 …
 \label{tab:fdetacceptance}
 \end{center}
 \end{table}
+\end{table*}
 …
 In addition, some detector data are added: tracks, calorometric towers and hits in \textsc{zdc}, \textsc{rp220} and \textsc{fp420}.
 While electrons, muons and photons are easily identified, some other objects are more difficult to measure, like jets or missing energy due to invisible particles.
+For most of these objects, their four-momentum $p^\mu$ and related quantities are directly accessible in \textsc{Delphes} output ($E$, $\vec{p}$, $p_T$, $\eta$ and $\phi$). Additional properties are available for specific objects (like the charge and the isolation status for $e^\pm$ and $\mu^\pm$, the result of application of $b$-tag for jets and time-of-flight for some detector hits).
 …
 Generator level muons entering the detector acceptance are considered as candidates for the analysis level.
 The acceptance is defined in terms of a transverse momentum threshold to overpass (default : $p_T > 0~\textrm{GeV}$) and of the pseudorapidity coverage of the muon system of the detector (default: $-2.4 \leq \eta \leq 2.4$).
 The application of the detector resolution on the muon momentum depends on a Gaussian smearing of the $p_T$ variable\footnote{\texttt{[code]} See the \texttt{SmearMuon} method.}. Neither $\eta$ nor $\phi$ variables are modified. Multiple scattering is thus neglected, while low energy muons have a worst resolution in a real detector.
+The acceptance is defined in terms of a transverse momentum threshold to overpass (default : $p_T > 10~\textrm{GeV}$) and of the pseudorapidity coverage of the muon system of the detector (default: $-2.4 \leq \eta \leq 2.4$).
+The application of the detector resolution on the muon momentum depends on a Gaussian smearing of the $p_T$ variable\footnote{\texttt{[code]} See the \texttt{SmearMuon} method.}. Neither $\eta$ nor $\phi$ variables are modified beyond the calorimeters: no additional magnetic field is applied. In addition, multiple scattering is also neglected. This implies that low energy muons have in \textsc{Delphes} a better resolution than in a real detector.
 \subsubsection*{Charged lepton isolation}
 To improve the quality of the contents of the charged lepton collections, additional criteria are applied to impose some isolation. This requires that the electron or muon candidate is isolated in the detector from any other particle, within a small cone. In \textsc{Delphes}, charged lepton isolation demands that there is no other charged particle with $p_T>2~\textrm{GeV}$ within a cone of $\Delta R<0.5$ around the lepton.\\
+To improve the quality of the contents of the charged lepton collections, additional criteria can be applied to impose some isolation. This requires that electron or muon candidates are isolated in the detector from any other particle, within a small cone. In \textsc{Delphes}, charged lepton isolation demands that there is no other charged particle with $p_T>2~\textrm{GeV}$ within a cone of $\Delta R = \sqrt{\Delta \eta^2 + \Delta \phi^2} <0.5$ around the lepton. The result (i.e. \textit{isolated} or \textit{not}) is added to the charged lepton measured properties\footnote{\texttt{[code] }See the \texttt{IsolFlag} output of the \texttt{Electron} or \texttt{Muon} collections in the \texttt{Analysis} tree.}.\\
 …
 Six different jet reconstruction schemes are available\footnote{\texttt{[code] }The choice is done by allocating the \texttt{JET\_jetalgo } input parameter in the smearing card.}. The first three belong to the cone algorithm class while the last three are using a sequential recombinaison scheme. For all of them, the towers are used as input of the jet clustering. Jet algorithms also differ with their sensitivity to soft particles or collinear splittings, and with their computing speed performance.
+\begin{itemize}
+\item \textbf{Cone algorithms:}
+\subsubsection*{Cone algorithms}
 \begin{enumerate}
 \item {\it CDF JetClu}: Algorithm forming jets by associating together towers lying within a circle (default radius $R=0.7$) in the $(\eta$, $\phi)$ space.
+\item {\it CDF Jet Clusters}: Algorithm forming jets by associating together towers lying within a circle (default radius $\Delta R=0.7$) in the $(\eta$, $\phi)$ space.
 The so-called \textsc{jetclu} cone jet algorithm that was used by \textsc{cdf} in Run II is used.
 All towers with a transverse energy $E_T$ higher than a given threshold (default: $E_T > 1~\textrm{GeV}$) are used to seed the jet candidates.
 The existing \textsc{FastJet} code as been modified to allow easy modification or the tower pattern in $\eta$, $\phi$ space.
 In the following versions of \textsc{Delphes}, a new dedicated plugin will be created on this purpose\footnote{\texttt{[code] }\texttt{JET\_coneradius} and \texttt{JET\_seed} variables in the smearing card.}.
+In the following versions of \textsc{Delphes}, a new dedicated plug-in will be created on this purpose\footnote{\texttt{[code] }\texttt{JET\_coneradius} and \texttt{JET\_seed} variables in the smearing card.}.
 \item {\it CDF MidPoint}: Algorithm developped for the \textsc{cdf} Run II to reduce infrared and collinear sensitivity compared to purely seed-based cone by adding `midpoints' (energy barycenters) in the list of cone seeds.
 …
 \end{enumerate}
+\item {\bf Recombination algorithms:}
+The three following infrared and collinear safe algorithms rely on recombination schemes where neighbouring calotower pairs are successively merged. The definitions of the jet algorithms are identical except for the distance used during the merging procedure. The jet reconstruction stars by finding the minimum value $d_{min}$ of all the distances $d_{ij}$ between each pair of towers and all `beam distance' $d_{iB}$. If the minimum distance is a $d_{ij}$ the towers are merged into a single tower, summing their four-momenta using the E-scheme recombination. If the minimum value is a $d_{iB}$, the object is declared as a final jet and is removed from the input list. This procedure is repeated until no input towers are left. More information on these jet can be found here.
+\subsubsection*{Recombination algorithms}
+The three following jet algorithms are safe for soft radiations (\textit{infrared}) and collinear splittings. They rely on recombination schemes where neighbouring calotower pairs are successively merged. The definitions of the jet algorithms are similar except for the definition of the \textit{distances} $d$ used during the merging procedure. Two such variables are defined: the distance $d_{ij}$ between each pair of towers $(i,j)$, and a variable $d_{iB}$ (\textit{beam distance}) depending on the transverse momentum of the tower $i$.
+The jet reconstruction algorithm browses the calotower list. It starts by finding the minimum value $d_\textrm{min}$ of all the distances $d_{ij}$ and $d_{iB}$. If $d_\textrm{min}$ is a $d_{ij}$, the towers $i$ and $j$ are merged into a single tower with a four-momentum $p^\mu = p^\mu (i) + p^\mu (j)$ (\textit{E-scheme recombination}). If $d_\textrm{min}$ is a $d_{iB}$, the tower is declared as a final jet and is removed from the input list. This procedure is repeated until no input towers are left. Further information on these jet algorithms is given here below, using $k_{ti}$, $y_{i}$ and $\phi_i$ as the transverse momentum, rapidity and azimuth of calotower $i$ and $\Delta R_{ij}= \sqrt{(y_i-y_j)^2+(\phi_i-\phi_j)^2}$ as the jet-radius parameter:
 \begin{enumerate}[start=4]
 …
 \item {\it Longitudinally invariant $k_t$ jet}:
 \begin{equation}
+d_{ij} = min(k_{ti}^2,k_{tj}^2)\Delta R_{ij}^2/R^2,
+\end{equation}
+with $\Delta R_{ij}^2= (y_i-y_j)^2+(\phi_i)-\phi_j)^2$, $k_{ti}$, $y_{i}$ and $\phi_i$ are the transverse momentum, rapidity and azimuth of calotower i and $R$ is the jet-radius parameter defined in the datacard. The beam distance is defined as $d_{iB}=k_{ti}^2$.
+\begin{array}{l}
+  d_{ij} = \min(k_{ti}^2,k_{tj}^2)\Delta R_{ij}^2/R^2 \\
+  d_{iB}=k_{ti}^2 \\
+\end{array}
+\end{equation}
 \item {\it Cambridge/Aachen jet}:
 \begin{equation}
+d_{ij} = \Delta R_{ij}^2/R^2,~d_{iB}=1.
+\end{equation}
+\item {\it Anti $k_t$ jet}: hard jets are exactly circular on Behaves like
+\begin{equation}
+d_{ij} =  min(1/k_{ti}^2,1/k_{tj}^2)\Delta R_{ij}^2/R^2,~d_{iB}=1/k_{ti}^2
+\end{equation}
+ \end{enumerate}
+\end{itemize}
+The reconstructed jets are conserved in the jet list if their transverse energy is bigger than {\verb PTCUT_jet }.
+By default, jets are reconstructed using a cone algorithm with $R=0.7$ and use the calorimetric towers. The reconstructed jets are required to have a transverse momentum above $20~\textrm{GeV}$ and $|\eta|<3.0$.
+\begin{array}{l}
+d_{ij} = \Delta R_{ij}^2/R^2\\
+d_{iB}=1 \\
+\end{array}
+\end{equation}
+\item {\it Anti $k_t$ jet}: where hard jets are exactly circular
+\begin{equation}
+\begin{array}{l}
+d_{ij} =  \min(1/k_{ti}^2,1/k_{tj}^2)\Delta R_{ij}^2/R^2 \\
+d_{iB}=1/k_{ti}^2 \\
+\end{array}
+\end{equation}
+\end{enumerate}
+By default, reconstruction uses a cone algorithm with $\Delta R=0.7$. Jets are stored if their transverse energy is higher\footnote{\texttt{[code] PTCUT\_jet }variable in the smearing card.} than $20~\textrm{GeV}$.
 \subsection{$b$-tagging}
 A jet is tagged as $b$-jets if its direction lies in the acceptance of the tracker and if it is associated to a parent $b$-quark. A $b$-tagging efficiency of $40\%$ is assumed if the jet has a parent $b$ quark. For $c$-jets and light/gluon jets, a fake $b$-tagging efficiency of $10 \%$ and $1 \%$ respectively is assumed\footnote{\texttt{[code] }Corresponding to the \texttt{TAGGING\_B}, \texttt{MISTAGGING\_C} and \texttt{MISTAGGING\_L} constants, for (respectively) the efficiency of tagging of a $b$-jet, the efficiency of mistagging a c-jet as a $b$-jet, and the efficiency of mistatting a light jet (u,d,s,g) as a $b$-jet.}
+A jet is tagged as $b$-jets if its direction lies in the acceptance of the tracker and if it is associated to a parent $b$-quark. A $b$-tagging efficiency of $40\%$ is assumed if the jet has a parent $b$ quark. For $c$-jets and light jets (i.e. originating in $u$,$d$,$s$ quarks or in gluons), a fake $b$-tagging efficiency of $10 \%$ and $1 \%$ respectively is assumed\footnote{\texttt{[code] }Corresponding to the \texttt{TAGGING\_B}, \texttt{MISTAGGING\_C} and \texttt{MISTAGGING\_L} constants, for (respectively) the efficiency of tagging of a $b$-jet, the efficiency of mistagging a $c$-jet as a $b$-jet, and the efficiency of mistagging a light jet ($u$,$d$,$s$,$g$) as a $b$-jet.}
 %(Fig.~\ref{fig:btag})
+.
 The (mis)tagging relies on the true particle \textsc{id} of the most energetic particle within a cone around the observed $(\eta,\phi)$ region, with a radius $R = \sqrt{\Delta \eta^2 + \Delta \phi^2}$ of $0.7$.
+The (mis)tagging relies on the true particle identity (\textsc{pid}) of the most energetic particle within a cone around the observed $(\eta,\phi)$ region, with a radius $\Delta R$ of $0.7$.
 %\begin{figure}[!h]
 …
 Jets originating from $\tau$-decays are identified using an identification procedure consistent with the one applied in a full detector simulation~\cite{bib:cmstaus}.
+\begin{wrapfigure}{l}{0.3\columnwidth}
+\includegraphics[width=0.3\columnwidth]{Tau}
+\caption{Illustration of the identification of $\tau$ jets.}
+The tagging rely on two properties of the $\tau$ lepton. First, $77\%$ of the $\tau$ hadronic decays contain only one charged hadron associated to a few neutrals (table~\ref{tab:taudecay}). Tracks are useful for this criterium. Secondly, the particles arisen from the $\tau$ lepton produce narrow jets in the calorimeter (\textit{collimation}).
+\begin{table}[!h]
+\begin{center}
+\caption{ Branching rations for $\tau^-$ lepton~\cite{bib:pdg}. $h^\pm$ and $h^0$ refer to charged and neutral hadrons, respectively. $n \geq 0$ and $m \geq 0$ are integers.
+\vspace{0.5cm}  }
+\begin{tabular}[!h]{ll}
+\hline
+ \multicolumn{2}{l}{\textbf{Leptonic decays}}\\
+ $ \tau^- \rightarrow e^- \ \bar \nu_e \ \nu_\tau$ & $17.85\% $ \\
+ $ \tau^- \rightarrow \mu^- \ \bar \nu_\mu  \ \nu_\tau$ & $17.36\%$ \\
+ \multicolumn{2}{l}{\textbf{Hadronic decays}}\\
+ $ \tau^- \rightarrow h^-\ n\times h^\pm \ m\times h^0\  \nu_\tau$  & $64.79\%$ \\
+ $ \tau^- \rightarrow h^-\ m\times h^0 \ \nu_\tau$  & $50.15\%$ \\
+ $ \tau^- \rightarrow h^-\ h^+ h^-  m\times h^0 \ \nu_\tau$  & $15.18\%$ \\
+\hline
+\end{tabular}
+\label{tab:taudecay}
+\end{center}
+\end{table}
+%\begin{wrapfigure}{l}{0.3\columnwidth}
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=0.6\columnwidth]{Tau}
+\caption{Illustration of the identification of $\tau$-jets. The jet cone is narrow and contains only one track.}
 \label{h_WW_ss_cut1}
+\end{wrapfigure}
+The tagging rely on two properties of the $\tau$ lepton. First, in roughly $75 \%$ of the time, the hadronic $\tau$-decay products contain only one charged hadron and a number of $\pi^0$. Secondly, the particles arisen from the $\tau$ lepton produce narrow jets in the calorimeter.
+\end{center}
+\end{figure}
+%\end{wrapfigure}
 \subsubsection*{Electromagnetic collimation}
+To use the narrowness of the $\tau$-jet, the \textit{electromagnetic collimation} ($C_{\tau}^{em}$) is defined as the sum of the energy in a cone with $\Delta R = ${\verb TAU_energy_scone } around the jet axis divided by the energy of the reconstructed jet. The energy in the small cone is calculated using the towers objects. To be taken into account a calorimeter tower should have a transverse energy above a given threshold {\verb JET_M_seed }. A large fraction of the jet energy, denominated here with {\verb TAU_energy_frac } is expected in this small cone. The quantity is represented in figure \ref{fig:tau1} for the default values (see table \ref{tab:tauRef}).
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=0.8\columnwidth]{figures/Tau2}
+\caption{\textcolor{red}{Distribution of the $\tau \bar \tau$ events} with respect to the electromagnetic collimation factor $C_\tau$. }
+To use the narrowness of the $\tau$-jet, the \textit{electromagnetic collimation} $C_{\tau}^{em}$ is defined as the sum of the energy of towers in a small cone of radius $R^\textrm{em}$ around the jet axis, divided by the energy of the reconstructed jet.
+To be taken into account, a calorimeter tower should have a transverse energy $E_T^\textrm{tower}$ above a given threshold.
+A large fraction of the jet energy is expected in this small cone. This fraction, or collimation factor, is represented in Fig.~\ref{fig:tau2} for the default values (see table \ref{tab:tauRef}).
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=\columnwidth]{Tau2}
+\caption{Distribution of the electromagnetic collimation $C_\tau$ variable for true $\tau$-jets, normalised to unity. This distribution is shown for associated $WH$ photoproduction~\cite{bib:whphotoproduction}, where the Higgs boson decays into a $W^+ W^-$ pair. Each $W$ boson decays into a $\ell \nu_\ell$ pair, where $\ell = e, \mu, \tau$.
+Events generated with MadGraph/MadEvent~\cite{bib:mgme}.
+Histogram entries correspond to true $\tau$-jets, matched with generator level data. }
+\label{fig:tau2}
+\end{center}
+\end{figure}
+\subsubsection*{Tracking isolation}
+The tracking isolation for the $\tau$ identification requires that the number of tracks associated to a particle with a significant transverse momentum is one and only one in a cone of radius $R^\textrm{tracks}$.
+This cone should be entirely pointing to the tracker to be taken into account. Default values of these parameters are given in table~\ref{tab:tauRef}.
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=\columnwidth]{Tau1}
+\caption{Distribution of the number of tracks $N^\textrm{tracks}$ within a small jet cone for true $\tau$-jets, normalised to unity. Photoproduced $WH$ events, where $W$ bosons decay leptonically ($e,\mu,\tau$), as in Fig.~\ref{fig:tau2}.
+Histogram entries correspond to true $\tau$-jets, matched with generator level data.}
 \label{fig:tau1}
 \end{center}
 \end{figure}
-\subsubsection*{$\tau$ selection using tracks}
-\begin{figure}[!h]
-\begin{center}
-\includegraphics[width=0.8\columnwidth]{figures/Tau1}
-\caption{\textcolor{red}{Distribution of the...}}
-\label{h_WW_ss_cut1}
-\end{center}
-\end{figure}
-The tracking isolation for the $\tau$ identification requires that the number of tracks associated to a particle with $p_T >$ {\verb TAU_track_pt } is one and only one in a cone with $\Delta R =$ {\verb TAU_track_scone }. This cone should be entirely included in the tracker to be taken into account. This procedure selects taus decaying hadronically with a typical efficiency of $60\%$. Moreover, the minimal $p_T$ of the $\tau$-jet is required to be {\verb TAUJET_pt } (default value: $10~\textrm{GeV}$).\\
 \begin{table}[!h]
 \begin{center}
+\begin{tabular}[!h]{llc}
+\hline
+Tau definition  & Card flag & Value\\\hline
+$\Delta R^{for~em}$     & {\verb TAU_energy_scone } & 0.15\\
+min $E_{T}^{tower}$     & {\verb JET_M_seed }  & 1.0~GeV\\
+$C_{\tau}^{em}$         & {\verb TAU_energy_frac } & 0.95.\\
+$\Delta R^{for~tracks}$ & {\verb TAU_track_scone } & 0.4\\
+min $p_T^{tracks}$      & {\verb PTAU_track_pt } & 2 GeV\\\hline
+\caption{Default values for parameters used in $\tau$-jet reconstruction algorithm. Electromagnetic collimation requirements involve the inner \textit{small} cone radius $R^\textrm{em}$, the minimum transverse energy for calotowers $E_T^\textrm{tower}$ and the collimation factor $C_\tau$. Tracking isolation constrains the number of tracks with a significant transverse momentum $p_T^\textrm{tracks}$ in a cone of radius $R^\textrm{tracks}$.  Finally, the $\tau$-jet collection is purified by the application of a cut on the $p_T$ of $\tau$-jet candidates.
+\vspace{0.5cm}  }
+\begin{tabular}[!h]{lll}
+\hline
+Parameter  & Card flag & Value\\\hline
+\multicolumn{3}{l}{\textbf{Electromagnetic collimation}} \\
+$R^\textrm{em}$     & \texttt{TAU\_energy\_scone } & $0.15$\\
+min $E_{T}^\textrm{tower}$     & {\verb JET_M_seed }  & $1.0$~GeV\\
+$C_{\tau}$         & \texttt{TAU\_energy\_frac} & $0.95$\\
+\multicolumn{3}{l}{\textbf{Tracking isolation}} \\
+$R^\textrm{tracks}$ & \texttt{TAU\_track\_scone} & $0.4$\\
+min $p_T^{tracks}$      & \texttt{PTAU\_track\_pt } & $2$ GeV\\
+\multicolumn{3}{l}{\textbf{$\tau$-jet candidate}} \\
+$\min p_T$ & \texttt{TAUJET\_pt} & $10$ GeV\\
+\hline
 \end{tabular}
 \label{tab:tauRef}
 …
 \end{table}
+\subsubsection*{Purity}
+Once both electromagnetic collimation and tracking isolation are applied, a threshold on the $p_T$ of the $\tau$-jet candidate is requested to purify the collection. This procedure selects $\tau$ leptons decaying hadronically with a typical efficiency of $60\%$.
 \subsection{Transverse missing energy}
+In an ideal detector, the transverse missing energy is simply computed as the missing term which would balance the transverse momentum in the observed event. Its value is then computed as the opposite of the sum of the momentum of all observed particles. In a real experiment, any problem affecting the detector (dead channels, misalignment, noisy towers, cracks) is directly worsening the measured missing transverse energy. In this document, the missing transverse energy (\textcolor{red}{symbol???}) is based on the calorimetric towers and only muons and neutrinos are not taken into account for its evaluation.
+In an ideal detector, the transverse momentum of the observed final state $p_T^\textrm{obs}$ should be equal to the $p_T$ sum of the invisible particles, written $p_T^\textrm{miss}$.
+\begin{equation}
+ p_T^\textrm{miss} = - p_T^\textrm{obs}
+\end{equation}
+the transverse missing energy would simply be computed as the term which balances the transverse momentum sum in the observed event. Its value is then computed as the opposite of the sum of the momentum of all observed particles. In a real experiment, any problem affecting the detector (dead channels, misalignment, noisy towers, cracks) is directly worsening the measured missing transverse energy. In this document, the missing transverse energy (\textcolor{red}{symbol???}) is based on the calorimetric towers and only muons and neutrinos are not taken into account for its evaluation.
 \section{Trigger emulation}
 …
 \section{Validation}
+\subsection{Jet resolution}
+The majority of interesting processes at the \textsc{lhc} contain jets in the final state. The jet resolution obtained using \textsc{Delphes} is therefore a crucial point of the validation. While \textsc{Delphes} contains six jet reconstruction algorithms, only the jet clustering algorithm with $R=0.7$ is used to validate the jet collection. Cross-check has been made with the results obtained using the \textsc{cms} detector. This validation employs $pp \rightarrow gg$ events produced using \textsc{mg/me} and hadronized using \textsc{pythia}. The events were divided into 14 bins of $\hat{p_T}$ of the gluons. Each \textsc{Delphes} jet is matched to the closest {\it particle-level} jet using the spatial separation in $\eta - \phi$ between the two jet axis $\Delta R<0.25$, otherwise they are discarded. The particle-level jets are obtained by applying the same clustering algorithm to all particles considered as stable by \textsc{pythia}.
+For each $\hat{p}_T$ bin, the  \textsc{Delphes} jet transverse energy ($E_T^{rec}$) of all jets satisfying the matching criteria is compaired to the {\it particle level} transverse energy ($E_T^{MC}$). The obtained histograms of the $E_T^{rec}/E_T^{MC}$ response have been fitted with a Gaussian function in the interval $\pm 2.RMS$ centered around the mean value. The final jet resolution is obtained using the following formula:
+\begin{equation}
+\frac{\sigma(R_{jet})}{<R_{jet}>}=\frac{\sigma(\frac{E_T^{rec}}{E_T^{MC}})_{fit}}{<\frac{E_T^{rec}}{E_T^{MC}}>_{fit}}.
+\end{equation}
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=\columnwidth]{resolutionJet}
+\caption{Distribution of the jet transverse energy resolution as a function of the {\it particle-level}  jet transverse energy. The maximum allowed separation between the \textsc{Delphes} and the {\it partile-level} jets is $\Delta R<0.25$.}
+\label{fig:jetresol}
+\end{center}
+\end{figure}
+The resulting jet resolution, plotted as a function of $E_T^{GEN}$ is shown in figure \ref{fig:jetresol}. The plots were then fitted with a function of the following form:
+\begin{equation}
+\frac{a}{E_T^{GEN}}\oplus \frac{b}{\sqrt{E_T^{GEN}}}\oplus c,
+\end{equation}
+where a, b, and c are the fit parameters. The obtained resolution is compared to the one obtained with a recent version of the simulation package of the CMS detector. Overall, the resolution curve of \textsc{Delphes} matches relatively well to those of \textsc{cms}.
+\subsection{$E_T^{mis}$ resolution}
+Because all major detectors at hadron colliders have been designed to be as mutch hermetic as possible in order to detect the presence of one or more neutrinos through apparent missing transverse energy, the resolution of the $E_T^{miss}$ obtained with \textsc{Delphes} is a crucial point. The samples used to study the transverse missing energy performance are identical to those used for the jet validation. The {\it particle-level} true transverse missing energy is calculated as the vector sum of the transverse momenta of all visible particles (or equivalently, to the vector sum of invisible particles). It should be noticed that the contribution to the transverse missing energy from muons is negligeable in the sample we are interested in.
+In order to obtain the x-component missing energy resolution ($E_x^{miss}$), the distribution of the difference between the \textsc{Delphes} and the {\it particle-level} $E_x^{miss}$ has been fitted with a Gaussian function. The resulting $E_x^{mis}$ is plotted in figure \ref{fig:resolETmis} as a function of the total visible transverse energy, defined as the scalar sum of transverse energy in all towers ($\Sigma E_T$).
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=\columnwidth]{figures/resolutionETmis}
+\caption{$\sigma(E^{miss}_{x})$ as a function on the scalar sum of all towers ($\Sigma E_T$) for $pp \rightarrow gg$ events.}
+\label{fig:resolETmis}
+\end{center}
+\end{figure}
+The resolution is observed to follow the form
+\begin{equation}
+\sigma_X = \alpha ~\Sigma E_T ~\mathrm{GeV}^{1/2},
+\end{equation}
+whith $\alpha$ is depending on the resolution of the calorimeters. Knowing that the expected transverse missing energy resolution expected using the \textsc{cms} detector for similar events is $\sigma_X = (0.6-0.7) ~ \Sigma E_T ~ \mathrm{GeV}^{1/2}$ with no pile-up (no extra simultaneous $pp$ collision occuring at the same bunch crossing), we can conclude that the resolution obtained by \textsc{Delphes} ( $\sigma_X = 0.68~ \Sigma E_T ~\mathrm{GeV}^{1/2}$) is in excellent agreement with the expectations of a general purpose detector.
+\subsection{$tau$-jet efficiency}
+with an efficiciency of about $50\%$ for the $\tau$-jets in CMS~\cite{bib:cmstauresolution}.
 \section{Visualisation}
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=\columnwidth]{Detector_Delphes_1}
+\caption{Layout of the generic detector geometry assumed in \textsc{Delphes}. The innermost layer, close to the interaction point, is a central tracking system (pink).
+It is surrounded by a central calorimeter volume (green) with both electromagnetic and hadronic sections.
+The outer layer of the central system (red) consist of a muon system. In addition, two end-cap calorimeters (blue) extend the pseudorapidity coverage of the central detector.
+The actual detector granularity and extension is defined in the user-configuration card. The detector is assumed to be strictly symmetric around the beam axis (black line). Additional forward detectors are not depicted.}
+\label{fig:GenDet}
+\end{center}
+\end{figure}
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=0.6\columnwidth]{Detector_Delphes_2b}
+\caption{Layout of the generic detector geometry assumed in \textsc{Delphes}. Open 3D-view of the detector with solid volumes. Same colour codes as for Fig.~\ref{fig:GenDet} are applied. Additional forward detectors are not depicted.}
+\label{fig:GenDet2}
+\end{center}
+\end{figure}
 …
 \section{Conclusion and perspectives}
+\newpage
+\begin{thebibliography}{99}
+\bibitem{bib:Delphes} \textsc{Delphes}, hepforge:
+\bibitem{bib:FastJet} \textsc{Fast-Jet},
+\bibitem{bib:SIScone} A practical Seedless Infrared-Safe Cone jet algorithm, G.P. Salam, G. Soyez, JHEP0705:086,2007.
+\bibitem{bib:Hector} \textsc{Hector},
+\bibitem{bib:Frog} \textsc{Frog},
+\bibitem{bib:CMSresolution} CMS IN 2007/053
+\bibitem{bib:Root} \textsc{Root} - An Object Oriented Data Analysis Framework, R. Brun and F. Rademakers, Nucl. Inst. \& Meth. in Phys. Res. A 389 (1997) 81-86, \url{http://root.cern.ch}
+\bibitem{bib:cmstaus} Tau reconstruction in CMS
+\bibitem{bib:whphotoproduction} WH photoproduction, S. Ovyn
+\bibitem{bib:mgme} Madgraph/Madevent
+\bibitem{bib:pdg} C. Amsler et al. (Particle Data Group), PL B667, 1 (2008) (URL: http://pdg.lbl.gov)
+\bibitem{bib:cmstauresolution} R. Kinnunen, \textit{Study of $\tau$-jet identification in CMS}, CMS NOTE 1997/002.
+\end{thebibliography}
+\onecolumn
 \appendix
 …
 \subsection{Running the \textsc{Frog} event display}
 \begin{itemize}
 \item If the { \verb FLAG_frog } was switched on, two files were created during the run of \textsc{Delphes}: {\verb DelphesToFrog.vis } and {\verb DelphesToFrog.geom }. They contain all the needed information to run frog.
 …
 \end{itemize}
-\begin{thebibliography}{99}
-\bibitem{bib:Delphes} \textsc{Delphes}, hepforge:
-\bibitem{bib:FastJet} \textsc{Fast-Jet},
-\bibitem{bib:SIScone} A practical Seedless Infrared-Safe Cone jet algorithm, G.P. Salam, G. Soyez, JHEP0705:086,2007.
-\bibitem{bib:Hector} \textsc{Hector},
-\bibitem{bib:Frog} \textsc{Frog},
-\bibitem{bib:CMSresolution} CMS IN 2007/053
-\bibitem{bib:Root} \textsc{Root} - An Object Oriented Data Analysis Framework, R. Brun and F. Rademakers, Nucl. Inst. \& Meth. in Phys. Res. A 389 (1997) 81-86, \url{http://root.cern.ch}
-\bibitem{bib:cmstaus} Tau reconstruction in CMS
-\end{thebibliography}
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